In the transformed function Eq. (REF ) we see that the first order relativistic correction under a Lorentz boost is exclusively odd in Matsubara frequency: The first order correction term contains terms of order \(\omega _n\) , \(\omega _n^3\) , and \(\omega _n^5\) .
This shows that for any finite boost \(\beta > 0\) , an odd-frequency component is induced dynamically in the anomalous Green function. The appearance of odd-frequency already at \(\mathcal {O}(\beta ^1)\)  reinforces the notion that odd-frequency pairing is a ubiquitous state. For comparison, spin-orbit coupling, which is known to occur in a wide variety of materials, is an effect which occurs at \(\mathcal {O}(\beta ^2)\)  [1]}, [2]}.
